This is old, but I thought I'd put my 2 cents in:
Rand worked with, or supported a lot of people that we'd consider libertarian: Mises, Hazlitt, Goldwater etc. Often times when she proclaimed her support or recommended their works, she was quick to point out that she thought these people's works were useful, but that she was often opposed to them on philosophical grounds. So as Rand saw, and I think most objectivists should see, that we can work with libertarians.
For the most part though, I still don't see much for objectivists to gain when dealing with libertarians in the grand scheme of things - objectivists would have to be working on the libertarians . Ayn Rand thought the problem with the Classical Liberal tradition and it's derivatives was the lack of a strong philosophical base on which Capitalism was founded and defended. Libertarianism doesn't really have a focus or interest on the issue. There is very little talk or interest in issues pertaining to metaphysics and epistemology. Since those foundations are often weak in libertarianism and non-existent, moral debates and arguments are almost always deduced from political arguments or history. Thus if a libertarian wants to defend Capitalism, he often finds himself defending capitalism in opposition to say communism, rather than an objectivist that defends capitalism based on the nature of knowledge and reason.
I generally like Libertarians, but I do see what Rand saw, that they were too eager to rush into politics, rather than to address philosophical issues, which is ironic, since among conservatives, they are often considered the most abstract-minded and intellectual. That said, it shows what seems to be the major problem with the right, which is a lack of faith in the mind's ability to solve political and institutional issues (which has been the case since Burke - so no surprises there), and thus the desire to default to tradition and faith when such problems present themselves. Alas, this is why in 2018, we have Trump dominating the Republican party.

This was the same argument the Sophists made...the response is Plato (definition) and Aristotle (Logic).
Ayn Rand made this argument about how many of the bad ideas in philosophy originate from the primacy of consciousness, where basically the mind creates reality and thus ethics. The key here, would have been to get the guy to admit that ethics exist independent of people by definition. Thus a person could have a value, and that value could still be wrong.

The Eric Garner case is interesting: people have forgotten that it was the outrage over the Eric Garner case that sparked the riots over the Michael Brown case. Garner happened first, but his grand jury case took longer to execute. It's highly unlikely that had Eric Garner's video not gone viral that the media would have made a big deal over the Mike Brown incident, and the amount of protests going on wouldn't be as high as it is now.
Ultimately, the problem with this whole case, is that we know had the cop who grabbed Eric Garner from the back of the neck been a civilian he would've been charged with manslaughter, regardless of the circumstance; people have gotten charged with manslaughter for far less. The issue at hand, is that there's really no objective law on what degree cops are allowed to use force in comparison to citizens, especially when that act of force initiates a death.